Positive solutions of an integro-differential equation in all space with singular nonlinear term
| Autor: | Mario Michele Coclite, Giuseppe Maria Coclite |
|---|---|
| Rok vydání: | 2008 |
| Předmět: |
Physics
Regular singular point Applied Mathematics Operator (physics) Mathematical analysis Mathematics::Analysis of PDEs existence of positive solutions Term (logic) Space (mathematics) singular nonlinearity Nonlinear system Integro-differential equations in all space Singular solution Integro-differential equation Integro-differential equations in all space singular nonlinearity existence of positive solutions asymptotic behavior Discrete Mathematics and Combinatorics asymptotic behavior Analysis Mathematical physics |
| Zdroj: | Discrete & Continuous Dynamical Systems - A. 22:885-907 |
| ISSN: | 1553-5231 |
| DOI: | 10.3934/dcds.2008.22.885 |
| Popis: | We prove the existence of a positive solution in $W_{loc}^{2,q}$ for a semilinear elliptic integro-differential problem in $\mathbb{R}^N.$ The integral operator of the equation depends on a nonlinear function that is singular in the origin. Moreover, we prove that the averages of the solution and its gradient on the balls $\{x\in\mathbb{R}^N; |x| \le R\}, R>0,$ vanish as $R\to \infty.$ |
| Databáze: | OpenAIRE |
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